The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.
The present invention relates generally to detectors, and in particular to the enhancement of a display by refining an approximation of the actual energy received at a detector.
The measurement of radiance underlies many operations in remote sensing such as determining spectral signature (e.g., via measuring spectral directional reflectance factor, R) and sensing spatial imagery. Since optical detectors measure irradiance, the radiance is inferred and not directly measured. As a result there is a problem in the processing of irradiance measurement data in order to determine radiance that does not appear to be directly addressed in the literature. These errors intrinsic to the scene being viewed are produced by the unpredictable non-uniform illumination of the instantaneous-field-of-view (IFOV) of the individual optical detectors in an array of such detectors comprising a sensor.
These considerations are applicable to both passive and active sensors and to sensing via reflected and/or emitted radiance. They are also applicable to almost all detectors in the visible, infrared and ultraviolet bands that are designed to respond to the total incident optical power in whatever wavelength or bandwidths they are sensitive. Further background is provided in the following references:
Dereniak, E. L. and G. D. Boreman, xe2x80x9cInfrared Detectors and Systems,xe2x80x9d John Wiley, NY, 1996, pp. 152-3.
Hoist, G. C., xe2x80x9cElectro-Optical Imaging System Performance,xe2x80x9d SPIE Opt. Eng. Press, 2000, pp. 6,201, and 203.
Kaufman, Y. J., xe2x80x9cThe atmospheric effect on remote sensing and its correction,xe2x80x9d Chap. 9 of xe2x80x9cTheory and Applications of Optical Remote Sensing,xe2x80x9d G. Asrar, Ed., John Wiley, NY, 1989, pp. 336-7.
McKenna, Charles M., Personal communication, May 1997.
Miller, J. L. and E. Friedman, xe2x80x9cPhotonics Rules of Thumb: Optics, Electro-Optics, Fiber Optics, and Lasers,xe2x80x9d McGraw-Hill, NY, 1996, p. 269.
Nicodemus, F. E., J. C. Richmond, et al., xe2x80x9cGeometrical considerations and nomenclature in reflectance,xe2x80x9d National Bureau of Standards, U.S. Dept. Commerce, 1977, p. 37.
Nussbaum, A. and R. A. Phillips, xe2x80x9cContemporary Optics for Scientists and Engineers,xe2x80x9d Prentice-Hall, Englewood Cliffs, N.J., Chap. 10, 1976, p. 273.
Schulz, M. and L. Caldwell, xe2x80x9cNonuniformity correction and correctability of infrared focal plane arrays,xe2x80x9d Infrared Phys. and Tech., 36, 1995, pp. 763-777.
Stover, J. C., xe2x80x9cOptical Scattering: Measurement and Analysis,xe2x80x9d 2nd ed., SPIE Opt. Eng. Press, 1995, pp. 12-19.
During operation, individual detectors record the total irradiance E in some spectral band illuminating the non-infinitesimal solid angle subtended by each of the detectors. This is normally used to calculate an average radiance (Lav) based on the presumption of a uniform illumination of that solid angle. Usually the pattern of illumination is in fact non-uniform. This non-uniformity is not, and probably cannot, in principle, be calibrated out by any in-lab, pre- or post-operational usage procedure. The reasons for this are that the non-uniformities: vary unpredictably with the specific portion of the particular scene being viewed, vary in an unpredictable way from detector to detector in the array since they are usually arranged to view different portions of the scene, and vary unpredictably from instant to instant for time-varying scenes and for arrays in relative motion with respect to the scenes being viewed.
The non-uniformity in illumination of the Instantaneous Field of View (IFOV) of a single detector can be due to relatively fine surface features, relatively small objects, changes in reflectance or emittance due to relatively abrupt changes in topography or ground or object composition, and relatively abrupt changes in surface altitude within the IFOV of a single detector. The IFOV is a function of individual detector geometry and other characteristics. This value is related to the projected solid angle of a detector indicative of the portion of a scene that the detector is capable of viewing at any one time. Both the IFOV and the projected solid angle are essentially dictated by the design of the sensor and need no further elaboration for their respective derivations.
Despite the variation in illumination within any one solid angle subtended by an optical detector, the single measured irradiance, E, from one detector produces a single output, i.e., a pixel in an image (for an imaging sensor) that has a single magnitude of brightness corresponding to Lav in the detector""s spectral band. This pixel covers a small, but non-infinitesimal, area of the image.
An image typically consists of an orderly array of a very large number of pixels that, when viewed as a whole, display the image. Irradiance (E) and radiance (L) are fundamentally related through the mathematical derivative relation                     L        =                              ⅆ            E                                ⅆ            Σ                                              (        1        )            
(where xcexa3=projected solid angle) and its inverse (integral) relation
E=∫Ldxcexa3xe2x80x83xe2x80x83(2)
This effectively leads to characterizing the illuminated detectors as averaging the unpredictable non-uniform radiance received over the various lines-of-sight within their IFOV. Only when the illumination of the detector""s IFOV is uniform or nearly so, is there little or no error from using a radiance/irradiance geometric relation specific to the detector geometry, to determine the radiance from the detector response.
In terms of average radiance incident on the ith detector, Lavi, (averaged over the projected solid-angle xcexa3i of the IFOV of the ith detector)                               L                      av            i                          =                              ∫                          θ              ⁢                              xe2x80x83                            ⁢                                                L                  i                                ⁡                                  (                                      θ                    ,                    Ω                                    )                                            ⁢                              ⅆ                                  Σ                  i                                                                          ∫                          ⅆ                              Σ                i                                                                        (        3        )            
(where xcex8=zenith angle and xcexa9=azimuth angle and dxcexa3i=cos xcex8i dxcex8i dxcexa9i) the irradiance illuminating the ith detector can be expressed as
Ei=xcexa3i(Lavi).xe2x80x83xe2x80x83(4)
Clearly, when Li (xcex8,xcexa9)=constant, then Li can be inferred from                               L          i                =                              E            i                                Σ            i                                              (        5        )            
However, when the unpredictable illumination of the IFOV is strongly non-uniform and the detector response still is related to the average radiance value, the user must consider what relationship that average radiance value has to his desired measure. Such a desired measure might be the peak radiance within the IFOV or the radiance along the line-of-sight through the geometric center of the IFOV or some other measure. The choice of measure will generally depend to what purpose the data will be applied. The difference between the desired and inferred measures is termed the error. Such errors contribute to image distortion.
Presently known procedures typically correct for extrinsic sources of non-uniform illumination fields for which exist some physical models to guide the correction. These extrinsic sources usually are contributed from one or more of the following mechanisms: platform motion; media lying between surface viewed (or ground) and platform (e.g., turbulence); and sensor optics and/or detectors.
In dealing with such causes of non-uniform illumination of individual detectors in an array, the physics of the phenomenon is invoked in a model to reduce the effect of non-uniform illumination. Assume that the non-uniformity of illumination is intrinsic to the scene viewed. Thus, a physical model of an intrinsic process cannot be invoked. A reference that provides a broad catalogue of error sources and effects is Holst, ibid.
A non-uniformity intrinsic to the viewed scene is similar to the spatial photoresponse non-uniformity of detector arrays in which the photoresponsivity of the individual detectors in the array have manufacturing differences to include unequal xe2x80x9cagingxe2x80x9d rates of component materials. That is referred to as pattern noise, contributed by variations among detectors. The error source addressed by a preferred embodiment of the present invention involves unpredictable spatial variations of illumination occurring within the IFOV of each detector that may also vary unpredictably with time.
There are many sources of errors and imagery distortions for remotely sensed imagery, both endogenous and exogenous. External sources of image errors and distortions are usually dominated by those due to the presence of the atmosphere and these are very much dependent on the state of the atmosphere through which the optical energy propagates as well as the wavelength bands being used.
The optical system between the array of detectors and the atmosphere also contributes significantly to the degradation of the image to be sensed by that array. The reduction of the number of ranges of spatial frequencies is conveniently characterized by the optical transfer function of this optical system. Care must be taken with this representation when it is extended to include the detectors because of their nonlinear characteristics.
There are a number of different classes of detectors, each of which has its detection performance hindered by a variety of noise mechanisms. Of all of these mechanisms, there is one that bears some very slight similarity with the unpredictable non-uniform illumination of the IFOV problem. It is the spatial photoresponse non-uniformity of the detector array itself that can cause a severe problem in the use of infrared focal plane arrays. It is referred to as a fixed pattern noise and is created by the unintended differences in photoresponsivity of the individual detectors in the array.
In a preferred embodiment of the present invention no errors due to the nature of processing are addressed. For example, there are errors from the digitizing of the received analog signal resulting in some lower bound on radiometric resolution. Certainly a suitably sized aperture can create a non-uniform distortion of an image, but that is a fixed structure associated with the imaging equipment.
Furthermore, normally each detector is being illuminated, at least in part, by some different portion of the overall scene being viewed by the array of detectors comprising the sensor. For a detector array in relative motion with respect to the scenes being observed, as usually occurs in remote sensing, the non-uniformity in illumination of the individual IFOVs continue to vary in time throughout a mission.
It is not just the unpredictable non-uniformity of the illumination of the IFOV that is the problem but also it""s the character of the illumination that can generate errors. For example, in the case of a variation in only one dimension, the illumination (i.e., the magnitude of the radiance) varies linearly with angle across the IFOV of a detector bounded by angles xcex8i and xcex8j, thus
Li(xcex8)=aixcex8i+bi,xcex8ixe2x89xa6xcex8xe2x89xa6xcex8jxe2x80x83xe2x80x83(6)
where ai and bi are constants. Then, assuming xcex8xcx9c0 so that cos xcex8xcx9c1 as is often the case.                               E          i                =                              ∫                          θ              ⁢                              xe2x80x83                            ⁢                                                L                  i                                ⁡                                  (                  θ                  )                                            ⁢                              ⅆ                θ                                              =                                                    (                                                      a                    i                                    2                                )                            ⁢                              xe2x80x83                            [                                                θ                  i                  2                                -                                  θ                  j                  2                                            ]                        +                                          (                                  b                  i                                )                            ⁢                              xe2x80x83                            [                                                θ                  i                                -                                  θ                  j                                            ]                                                          (        7        )            
Dividing Eqn. (7) by [xcex8i-xcex8j] produces the average value of Li (xcex8) in the range of xcex8located at the midpoint between xcex8i-xcex8j,                                           E            i                                [                                          θ                i                            -                              θ                j                                      ]                          =                                                                              (                                      a                    i                                    )                                ⁢                                  xe2x80x83                                ⁢                                  ⌊                                                            θ                      i                                        -                                          θ                      j                                                        ⌋                                            2                        +                          (                              b                i                            )                                =                      L                          av              i                                                          (        8        )            
Thus if in the application of interest all that is required is that the measured value produces the average value of radiance at the center of the pixel, no distortion or error is produced. However, this is seldom the case for xe2x80x9creal-worldxe2x80x9d measurements.
Accordingly, a method is needed for determining approximate peak and valley radiance values in symmetric cases from measurement data as well as approximate values at the detector geometric surface centers for non-monotonically increasing and decreasing segments of the radiance fields. The method is also needed to deal with the effects of unpredictable, non-uniform illumination of detectors caused by any number of different environmental conditions or characteristics of the scene being viewed by the detectors.
Accordingly, it is an object of the present invention to improve numerical accuracy of quantitative imaging.
It is another object of the present invention to increase image contrast.
It is a further object of the present invention to decrease spatial blurring of images.
It is an additional object of the present invention to increase image resolution without a corresponding decrease in detector FOV and increase in the number of detectors in the array.
It is still an additional object of the present invention to reduce the effects of the unpredictable, non-uniform illumination of detector IFOV caused by the specific scene viewed by that detector.
It is again another object of the present invention to reduce distortion as the scene viewed changes in an unpredictable way with time.
It is yet an additional object of the present invention to reduce distortion for all the detectors within an array of detectors even though each may be sensing a different non-uniformity because they are viewing different portions of a scene.
It is still a further object of the present invention to reduce errors from an error source that cannot be calibrated out in advance of, or after, detector array usage in any of the conventional ways.
It is yet another object of the present invention to reduce errors from an error source intrinsic to the scene viewed and for which no other method exists.
It is still an additional object of the present invention to improve the probability of detecting relatively small objects, fine surface features and abrupt changes in reflectance and/or emittance due to abrupt changes in ground or object composition.
It is yet another object of the present invention to reduce errors associated with rapid, moderate and slow variations in illumination non-uniformity occurring within each detector""s IFOV.
It is an object of the present invention to improve the accuracy of pixel de-mixing.
These and other objects and goals of the present invention are achieved by a method of adjusting the output of an array of optical detectors to improve a derived approximation of the radiance value provided by each detector to compensate for non-uniform illumination at each detector.